VA Metering in Delta-Wired Electrical Service

ABSTRACT

An arrangement includes an A/D converter and a processing circuit. The A/D converter is configured to generate digital samples of voltage and current waveforms in a polyphase electrical system. The processing circuit is operably coupled to receive the digital samples from the A/D converter. The processing circuit configured is to obtain contemporaneous phase current and voltage samples I A , I B , I C  and/or I N , and V A , V B , V C . The processing circuit is further configured to determine at least I CB  sample values based on three of the current samples of I A , I B , I C , and I N , and determine a VA value based at least in part on I CB . The processing circuit is further configured to provide information representative of the VA calculation to one of a group consisting of a display, a communication circuit, a memory and a billing calculation unit.

FIELD OF THE INVENTION

The present invention relates generally to electricity measurements, andmore particularly, to apparent power (VA) and apparent energy (VAh)measurements.

BACKGROUND

One of the goals of electricity metering is to accurately measure theuse or consumption of electrical energy resources. With suchmeasurements, the cost of generating and delivering electricity may beallocated among consumers in relatively logical manner. Another goal ofelectricity metering is help identify electrical energy generation anddelivery needs. For example, cumulative electricity consumptionmeasurements for a service area can help determine the appropriatesizing of transformers and other equipment.

Electricity metering often involves the measurement of consumed power orenergy in the form of watts or watt-hours. Real energy or active energymeasurements (expressed in watt-hours or wh) relate directly to theactual energy that the load requires. However, the amount of wattssupplied to a load does not necessarily reflect the amount of power thatmust be produced by the source. In particular, the amount of load watts,or load watt-hours, does not necessarily accurately relate to the sizeof the service (transformers size, size of power lines, etc.) needed tosupply the load. This is due in part to loads that have significantcapacitive and/or inductive components. In such loads, the actual energyconsumption in watt-hours can be significantly less than the apparentenergy (expressed as “VA-hours” or “VAh”) that must be produced by theenergy source.

For example, consider two loads: a first load consuming 240 watts at 120volts and which is completely resistive, and a second load consuming 240watts at 120 volts and having a phase difference between voltage andcurrent of 30°. Using the basic AC power consumption equation

Watts=V _(rms) I _(rms) cos θ,  (1)

, where θ is the phase angle between voltage and current, it can be seenthat the first load requires 2 amps of current because I=240/(120*cos0°), while the second load requires 2.31 amps of current becauseI=240/(120*cos 30°). While the actual watt-hour consumption of thesecond load is the same as the first load, the second load requires morecurrent, which can affect sizing of power lines, transformers, etc.Consequently, it can be desirable to measure VA or VAh to help indetermining the size of the source, i.e. transformers size, size of thepower lines, etc., needed to supply the load.

Moreover, in a case of a customer that consumes significantly more VAthan watts, the metering of only watt-hours will not accurately identifythe customer's proportional cost of the power delivery equipment. Forthis reason a more complex rate structure involving VA or VA-hours isoften used to recover the investment costs for such items astransformers and power lines etc. providing energy to the load. As aconsequence, many electricity meters, particularly for largernon-residential loads, have at least some capability to measure VA orVA-hours.

The calculation of VA or VA-hours in single phase systems is relativelystraight forward when the signals are pure sine waves. However, ifharmonics are present in the power line signal, then the calculations ofVA and the practical significance of the calculated VA becomes morecomplex.

One common method of calculating VA involves multiplying the RMS voltageby the RMS current, or in other words VA=V_(RMS)*I_(RMS). Converting VAto VA-hours, as is well known in the art, merely involves integratingthe VA values over time. For example, the VA value may be calculated at0.333 second intervals, with each calculation considered to be the VAconsumption over that 0.333 second, or approximately 1/10,800^(th) of anhour. These values are then accumulated to provide a running meter ofconsumed VA-hours. Because such calculations are routine, the terms VAand VA-hours may be used somewhat interchangeably herein, with theunderstanding that VA-hours may always be calculated from VA values.

In any event, a second common method of calculating VA involves firstdetermining the value of the reactive power, also known as VAR (Volt AmpReactive), and the real or active power in watts. The VAR value may becalculated using the equation VAR=V_(RMS)*I_(RMS)*sin θ, or by samplingvoltage and current and multiplying samples of voltage and current thatare 90° phase separated in the AC line cycle. The method then involvesderiving VA using the formula VA=√{square root over (Watt²+VAR²)}. Ifharmonics are present in the power line signal, then the use of theformula VA=√{square root over (Watt²+VAR²)} to calculate VA will yield aresult that is less than that calculated from the RMS values of voltageand current, VA=V_(RMS)*I_(RMS). Because of this inaccuracy, sometimes a3^(rd) quantity, distortion power (DP) is sometimes added as follows:

VA=√{square root over (Watt² +VAR ² +DP ²)}.  (2)

The above equations relate generally to single phase systems. In apolyphase system, the calculation of VA is more complex and thepractical significance of what is calculated goes beyond that of singlephase systems. In particular, the two methods of calculating VA (or VAh)described above for single phase systems do not necessarily yield thesame results if applied to polyphase systems even under conditions ofpure sine wave signals.

In one method, VA is calculated from the RMS values of the individualphase voltages and currents for each of a polyphase system, and then theVA value for the different phases is totaled. In other words, the VA ofeach phase is determined using VA=V_(RMS)*I_(RMS) and then the total VAis calculated by simply adding the individual VA of each phase. Thismethod of calculating VA is sometimes referred to as “RMS VA” (VA_(RMS))or “arithmetic VA”. Arithmetic VA is identified as being most accuratewith respect to the source or service side of the electrical system, andnot the load side.

In another method, the VA is calculated using watts and VAR. In thismethod, the total amount of watts for all three phases is determined,and the amount of VAR for all three phases is determined. The total VAis then calculated using the formula VA=√{square root over (Watt²+VAR²)}where Watt and VAR represent the total load watt and VAR respectively.This method of calculating VA is sometimes referred to as “vector VA”(VA_(V)). Vector VA is considered to be more accurate with the load sideof the electrical system.

Further detail regarding the calculation of arithmetic or source VA andthe calculation of vector or load VA for many types of electricalservice is provided in U.S. Pat. No. 7,747,400, which is incorporatedherein by reference in its entirety. In U.S. Pat. No. 7,747,400, a meteris disclosed that includes various methods of calculating that can beselected by a technician.

While the meter disclosed in U.S. Pat. No. 7,747,400 provides manyuseful metered VA values, it does not provide a source or arithmetic VAcalculation for four-wire delta electrical services. Accordingly, thereis a need for a meter that can calculate, among other things, VA infour-wire delta electrical services. Other known methods are inaccurate,particularly for unbalanced loads.

A particular need is for a method of measuring VA that accuratelyestimates or represents the VA at the source, which can provide betterinformation for the sizing of transformers and other equipment.

SUMMARY OF THE INVENTION

A first aspect of the invention is a meter that is operable to implementan appropriate VA calculation within an electricity meter in a four-wireservice based on values normally measurable and available within themeter.

At least one embodiment of the invention is an arrangement that includesan A/D converter and a processing circuit. The A/D converter isconfigured to generate digital samples of voltage and current waveformsin a polyphase electrical system. The processing circuit is operablycoupled to receive the digital samples from the A/D converter. Theprocessing circuit configured is to obtain contemporaneous phase currentand voltage samples I_(A), I_(B), I_(C) and/or I_(N), and V_(A), V_(B),V_(C). The processing circuit is further configured to determine atleast I_(CB) sample values based on three of the current samples ofI_(A), I_(B), I_(C), and I_(N), and determine a VA value based at leastin part on I_(CB). The processing circuit is further configured toprovide information representative of the VA calculation to one of agroup consisting of a display, a communication circuit, a memory and abilling calculation unit.

In another embodiment, the processing circuit is further configured togenerate the I_(CB) sample value based on the equation⅙I_(B)−⅙I_(A)+½I_(C). In still other embodiments, the processing circuitis further configured to generate a plurality of the I_(CB) samplevalues, and generate a magnitude value of the plurality of the I_(CB)sample values.

In another embodiment, the processing circuit is further configured todetermine the VA value further using a magnitude of the voltage fromphase C to phase B, and is configured to obtain the voltage magnitude bygenerating a plurality of the V_(CB) sample values, each C_(CB) samplevalue comprising a difference between a phase C sample and acontemporaneous phase B sample, and generating a V_(CB) magnitude valueusing the plurality of the V_(CB) sample values.

In yet another embodiment, the processing circuit then determines the VAvalue based at least in part on the product of the generated magnitudevalue of the current from phase C to phase B on the source side, and amagnitude of a voltage from phase C to phase B.

In another embodiment, the processing circuit is further configured togenerate an I_(CA) sample value based on the equation⅙I_(B)−⅙I_(A)+½I_(c). In still other embodiments, the processing circuitis further configured to generate a plurality of the I_(CA) samplevalues, and generate a magnitude value of the plurality of the I_(CA)sample values.

In another embodiment, the processing circuit is further configured todetermine the magnitude of the voltage from phase C to phase A bygenerating a plurality of the V_(CA) sample values, each V_(CA) samplevalue comprising a difference between a phase C sample and acontemporaneous phase A sample, and generating a V_(CA) magnitude valueusing the plurality of the V_(CA) sample values.

In yet another embodiment, the processing circuit then determines the VAvalue based at least in part on the product of the generated magnitudevalue of the current from phase C to phase A on the source side, and amagnitude of a voltage from phase C to phase A.

In another embodiment, the processing circuit is further configured togenerate the I_(BN) sample value based on the equation⅚I_(B)+⅙I_(A)+½I_(C). In still other embodiments, the processing circuitis further configured to generate a plurality of the I_(BN) samplevalues, and generate a magnitude value of the plurality of the I_(BN)sample values.

In yet another embodiment, the processing circuit then determines the VAvalue based at least in part on the product of the generated magnitudevalue of the current from phase B to neutral on the source side, and amagnitude of a voltage on phase B.

In another embodiment, the processing circuit is further configured togenerate the I_(AN) sample value based on the equation⅚I_(A)+⅙I_(B)+½I_(C). In still other embodiments, the processing circuitis further configured to generate a plurality of the I_(AN) samplevalues, and generate a magnitude value of the plurality of the I_(AN)sample values.

In yet another embodiment, the processing circuit then determines the VAvalue based at least in part on the product of the generated magnitudevalue of the current from phase A to neutral on the source side, and amagnitude of a voltage on phase A.

In some embodiments, the processing circuit is further configured togenerate the VA value based on the equation:

VA=|{right arrow over (V_(CB))}|*|{right arrow over (I _(CB))}|+|{rightarrow over (V _(CA))}|*|{right arrow over (I _(CA))}|+|{right arrow over(V _(B))}|*|{right arrow over (I _(BN))}|+|{right arrow over (V_(A))}|*|{right arrow over (I _(AN))}|

wherein {right arrow over (V_(CB))} is a vector value of the voltagefrom phase C to phase B, {right arrow over (I_(CB))} is vector valuerepresentative of the current from phase C to phase B at the source,{right arrow over (V_(CA))} is a vector value of the voltage from phaseC to phase A, {right arrow over (I_(CA))} is a vector valuerepresentative of the current from phase C to phase A at the source,{right arrow over (V_(B))} is a vector value of the voltage from phase Bto neutral, {right arrow over (I_(BN))} is a vector value representativeof the current from phase B to neutral at the source, {right arrow over(V_(A))} is a vector value of the voltage from phase A to neutral, and{right arrow over (I_(AN))} is a vector value representative of thecurrent from phase A to neutral at the source.

The above described features and advantages, as well as others, willbecome more readily apparent to those of ordinary skill in the art byreference to the following detailed description and accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an exemplary meter that may be used in one or moreembodiments of the present invention;

FIG. 2 shows a measurement arrangement in which an embodiment of theinvention may be employed; and

FIGS. 3A-3C show a flow diagram of the operation of a processing circuitof an arrangement for calculating VA in accordance with at least oneembodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 shows an exemplary embodiment of a polyphase electricity meter 10in which an arrangement according the invention is implemented.Referring to FIG. 1 specifically, the meter 10 is an apparatus formeasuring energy consumption that includes a scaling circuit 110, ananalog-to-digital conversion (“ADC”) circuit 114, a processing circuit116, a communication circuit 118, an optional display 120 and a datastore 112. All of the above listed elements are preferably supported bya meter housing 113, which may take a plurality of known forms. Thecommunication circuit 118 may be disposed within an interior of themeter housing 113 like the other devices, or may be affixed to theoutside of the meter housing 113.

In the embodiment described herein, the scaling circuit 110 and the ADCcircuit 114 are arranged to generate digital signals representative ofline voltage waveforms V_(A), V_(B), V_(C) for each of three phases A,B, C of a four-wire delta electrical system and other digital signalsrepresentative of at least three of the four line current waveformsI_(A), I_(B), I_(c) and I_(N) of the four-wire delta electrical system.As will be discussed below, however, the meter 10 may readily beconfigured for a three-wire delta electrical service, as well as othertypes of electrical service. The digital signals are typically sequencesof digital samples representative of an instantaneous voltage or currentmeasurement on one phase with respect to either neutral or anotherphase. Circuits capable of generating such signals are known in the art.

The processing circuit 116 is configured to calculate one or more energyconsumption values based on the digital signals. The energy consumptionvalues may be communicated to a remote device using the communicationcircuit 118, displayed using the display 120, stored in the data store112, or preferably some combination of the foregoing. In accordance withthe embodiments described herein, the processing circuit 116 is furtheroperable to perform any or all of the VA calculations described herein.

In a further detailed description of the meter 10 of FIG. 1, the scalingcircuit 110 may suitably comprise current and voltage sensors, notshown. The voltage sensors, which may, for example, include voltagedividers, generate a scaled down version of the voltage present onphases of the power lines 12. The current sensors, which may suitablyinclude current transformers, shunts, embedded coil devices and thelike, generate a voltage or current signal that is a scaled down versionof the current present on the phases of the power lines 12. Variousvoltage and current sensors are known in the art.

The ADC circuit 114 includes one or more analog-to-digital convertersthat convert the scaled measurement signals into digital voltage andcurrent measurement signals. Many circuits capable of generating digitalvoltage and circuit waveform signals are well known in the art. Suitableexamples of analog to digital conversion circuits having suchcapabilities are described in U.S. Pat. No. 6,374,188; U.S. Pat. No.6,564,159; U.S. Pat. No. 6,121,158 and U.S. Pat. No. No. 5,933,004, allof which are incorporated herein by reference. Moreover, the ADC circuit114 may readily be a part of an integrated metering chip package, aswill be discussed below.

The processing circuit 116 is a device that employs one or moreprocessing devices such as microprocessors, microcontrollers, digitalsignal processors, discrete digital circuits and/or combinationsthereof. As mentioned above, the processing circuit 116 is operable togenerate energy consumption data based on the digital signals. In oneexample, the processing circuit 116 generates watt-hour informationbased on an accumulation of products of contemporaneous voltage andcurrent samples. For example, true watt-hours for a particular phase maybe calculated as the vector product of the current waveform and thevoltage waveform. This vector product may be carried out with sampledvoltage (V_(n)) and sampled current (I_(n)) by the formula:

Whrs=ΣV _(n) *I _(n).  (3)

where Whrs is an accumulated energy value (i.e. watt-hours) for a timeframe from a starting time no to a time corresponding to n.

In addition, the processing circuit 116 preferably calculates VA and/orVAh using one or more of the methods described herein. Thus, theprocessing circuit 116 may generate VA, VAh, watt-hours, VAR-hrs, powerfactor, root-mean-square voltage and/or current, or combinations of anyof the foregoing. Various processing circuits operable to generateenergy consumption data from digital voltage and digital currentmeasurement signals are well known in the art. Suitable examples of suchcircuits are described in U.S. Pat. No. 6,374,188; U.S. Pat. No.6,564,159; U.S. Pat. No. 6,121,158 and U.S. Pat. No. 5,933,004. However,in one preferred embodiment, the processing circuit is (or includes) aprocessing element of a metering integrated circuit chip such as theTeridian 71M6533 measurement chip (available from Maxim). In thatembodiment, both the ADC circuit 114 and the processing circuit 116 aredisposed within the same semiconductor package.

More specifically, the processing circuit 116 in one embodiment isconfigured (i.e. programmed and/or arranged) to generate a first VAcalculation if configuration data identifies that a source VAcalculation is selected, the first VA calculation providing adetermination of a VA quantity that more accurately represents a sourceVA than a corresponding determination of a second VA calculation. Theprocessing circuit 116 is also configured to generate a second VAcalculation if the configuration data identifies that load VA isselected, the second VA calculation providing a determination of a VAquantity that more accurately represents a load VA than a correspondingdetermination of the first VA calculation. The configuration dataidentifying whether a source VA or load VA is to be calculated maysuitably be stored in the data store 112 or other memory, or merely bestored in a buffer or register that receives user input or acommunication input. The processing circuit 116 is further operable toprovide the VA calculation to one of a group consisting of the display120, the communication circuit 118, and a billing calculation unitwithin the processing circuit 116 or elsewhere.

To this end, the processing circuit 116 is configured to prompt the userto select either “source VA” or “load VA”, or some other indication thatVA is to be calculated from the perspective of the electricity source,or from the perspective of the load. The prompting may occur viainteractive display using the display 120 and the communication circuit118, or by other means. For example, the meter 10 may be configured in aconfiguration facility, not shown, but which are known in the art, whereconfiguration information (e.g. types of measurements to be taken,display features and/or calibration information) is programmed to amemory (i.e. data store 112). In accordance with some embodiments of theinvention, the configuration operation would further include selectionof “source VA” or “load VA”. To this end, the meter display 120 (or anexternal configuration device display, not shown) would provide the userwith a selection of whether a VA calculation should be one that isrepresentative of “source VA”, or whether the VA calculation should beone that is representative of “load VA”. The user would then program themeter with a selection based on whether source VA or load VA is desired.

When the meter 10 is subsequently installed for use, the meter 10performs a VA determination based on the stored configurationinformation of the user selection. If the user had selected source VA,then the processing circuit 116 automatically configures its meteringoperation to perform an arithmetic VA calculation. If, however, the userhad selected load VA, then the processing circuit 116 automaticallyconfigures its metering operation to perform a vector VA calculation.

The processing circuit 116 is further operable to store the plurality ofenergy consumption values in the data store 112. In some embodiments,the processing circuit 116 may store energy consumption values for eachof plurality of time periods, in order to allow analysis of energy usageat different times of day, days of the week or month, or evenseasonally. The storage of consumption indexed to time periods is oftenreferred to in the industry as “load profiling”. The data store 112 maysuitably be a random access memory, EEPROM, other memory, or acombination of several types of memory. In still other embodiments, thedata store 112 may include a circular buffer, FIFO device, or othermemory that stores data in the order in which it is received. Otherknown methods may be used. In at least some embodiments, the data store112 includes memory located within the integrated package that housesthe processing circuit 116. The data store 112 also includes a softwareprogram that is executed by the processing circuit 116 to perform theoperations of the processing circuit 116 described herein, includingthose of FIGS. 3A-3C.

The communication circuit 118 is a device that is in some embodimentsconfigured to communicate data between the metering unit 12 and one ormore remote devices. In a system such as that shown in FIG. 1, thecommunication circuit 118 would be operable to communicate directly orindirectly with a data collection system of a utility service provider.Several of such systems are known. The utility service provider thenuses the collected data to generate billing information and/or dataforecasting information as is known in the art. To this end, thecommunication circuit 118 may suitably include a radio, a telephonemodem, a power line carrier modem, or other known communication deviceconfigured for use with utility meters. Radios may be used that operatein the 100 MHz to 1 GHz range. However, other devices may operate in thekHz or low MHZ range. In addition or in the alternative, thecommunication circuit 118 is configured to communicate with a locallycoupled device, such as a reed switch, portable computing device, orother device. The communication circuit 118 may include an optical orelectrical data port, not shown, for this purpose.

The meter display 120, which is optional, may be a digital display suchas a liquid crystal display. It will be appreciated that the exactnature of the display is not particularly important to theimplementation of the invention. Nevertheless, there is an advantage ofincluding at least some display capabilities. LCD displays, moreover,have been found to have a particularly advantageous set of qualities foruse in electronic meters.

As discussed above, the processing circuit 116 in one embodiment isconfigured to generate a selected one of a source VA value or a load VAvalue. This value may be used for billing purposes, for planningpurposes and/or other analysis purposes. The VA value may be blendedwith other values, such as watt-hours or watts, or even reactive power.

As also discussed above, if a source VA is to be implemented, then theprocessing circuit 116 performs an arithmetic VA calculation. If a loadVA is to be implemented, then the processing circuit 116 performs avector VA calculation. As discussed above, as well as in U.S. Pat. No.7,747,400, the vector VA is a fundamentally different calculationcompared to arithmetic VA and sometimes yields different results. Ingeneral, the processing circuit 116 may be configured to determinevector or arithmetic VA for single phase, four-wire wye, and three-wiredelta systems as discussed in the U.S. Pat. No. 7,747,400. Moreover, theprocessing circuit 116 may determine the vector VA or load VA asdiscussed further above and as is known in the prior art. The VA valuesmay suitable be accumulated over time to provide VAh as is known.

However, in contrast to the prior art, at least some embodiments of theinvention determine source VA (i.e. and/or VAh) as discussed below inconnection with FIGS. 2 and 3A-3C.

FIG. 2 show a schematic representation of the meter 10 coupled between asource 200 and a load 201 in a four-wire delta electrical service. Thefour-wire delta electrical source 200 includes a delta power source(transformer) as is known in the art. The electrical source 200 isoperably coupled to provide three-phase delta-wired electrical serviceto the load 201 via a phase A line 212, a phase B line 214, a phase Cline 216 and a neutral line 218 defined between the phase A line 212 andthe phase B line 214. As is known in the art, the meter 10 generallymeters the energy (and related values) delivered to the load 201 fromthe source 200. The load 201 includes elements of a customer load, andmay include resistive, inductive and/or capacitive loads. The load 201may be balanced, or may be imbalanced, meaning that different loads maybe connected from phase A to phase B, from phase B to phase C, fromphase C to phase A, and/or additional loads may be connected from phaseA to neutral, phase B to neutral and/or phase C to neutral.

In general, the meter 10 is operably connected to obtain the voltagemeasurements V_(A), V_(B), and V_(C), and the current measurementsI_(A), I_(B), I_(C) and I_(N). More specifically, the scaling unit 110is operably coupled to generate voltage measurement signals V_(A),V_(B), V_(C), I_(A), I_(B), I_(C) and I_(N), and provide those signalsto the ADC circuit 114. In several embodiments described herein, onlythree of the four current values I_(A), I_(B), I_(C) and I_(N) need bedigitized and stored. Typically I_(N) is not digitized.

The signal V_(A) represents a scaled version of the voltage from thephase A line 212 to neutral 218. The signal V_(B) represents a scaledversion of the voltage from the phase B line 214 to neutral 218, and thesignal V_(C) represents a scaled version of the voltage from the phase Cline 216 to neutral 218. The signal I_(A) represents a scaled version ofthe current on the phase A line 212, signal I_(B) represents a scaledversion of the current on the phase B line signal 214, and I_(C)represents a scaled version of the current on the phase C line 216. Thesignal I_(N) represents a scaled version of the current on the neutralline 218.

The ADC circuit 114, in turn, samples each of the waveforms V_(A),V_(B), V_(C), I_(A), I_(B), I_(C) and I_(N), and generates correspondingdigital sample streams V_(A)(s), V_(B)(s), V_(C)(s), I_(A)(s), I_(B)(s),I_(c)(s), and I_(N)(s). The value s represents a sample index, whichcorresponds directly to a time increment. The sample rate s/sec istypically many times the cycle frequency of the AC waveform, such thatthe samples collective provide an accurate sampled representation of thecorresponding analog waveform. The operations of the scaling unit 110and the ADC circuit 114 as discussed above are conventional.

The processing circuit 116 then calculates load watt-hrs by multiplyingthe voltage vector of each phase with the current vector of each phase,and accumulating the resulting products. Using sampling, the processingcircuit 116 may suitably perform the following calculations:

Watt-hr_(A)=Σ(V _(A)(s)*I _(A)(s))  (5)

Watt-hr_(B)=Σ(V _(B)(s)*I _(B)(s))  (6)

Watt-hr_(C)=Σ(V _(C)(s)*I _(C)(s))  (7)

Watt-h=Watt-hr_(A)+Watt-hr_(B)+Watt-hr_(C)  (8)

wherein V_(x)(s) is the sampled voltage at a time s on phase x at themeter 10, and I_(x)(s) is the sampled current at a time s on phase x atthe meter 10. In the above equations, the term Watt-hr is actually anenergy measurement in terms of watt-hrs.

The processing circuit 116 may suitably calculate vector (or load) VARsusing the equation using 90 phase degree delayed current measurements,as is known.

VAR _(A)=Σ(V _(A)(s)*I _(A)(s−90°))  (9)

VAR _(B)=Σ(V _(B)(s)*I _(B)(s−90°))  (10)

VAR _(C)=Σ(V _(C)(s)*I _(C)(s−90°))  (11)

VAR=VAR _(A) +VAR _(B) +VAR _(C)  (12)

With these two values Watt-hr and VAR, the vector Vector_VA may becalculated as:

Vector_(—) VA=√{square root over (Watt² +VAR ²)}  (13)

On the other hand, the processing circuit 116 calculates source VA orarithmetic VA using the following vector equation:

SVA=VA=|{right arrow over (V_(CB))}|*|{right arrow over(I_(CB))}|+|{right arrow over (V_(CA))}|*|{right arrow over(I_(CA))}|+|{right arrow over (V_(B))}|*|{right arrow over(I_(BN))}|+|{right arrow over (V_(A))}|*|{right arrow over(I_(AN))}|  (14)

wherein {right arrow over (V_(CB))} is a vector value of the voltagefrom phase C to phase B, {right arrow over (I_(CB))} is representativeof the current from phase C to phase A at the source 200, {right arrowover (V_(CA))} is a vector value of the voltage from phase C to phase A,{right arrow over (I_(CA))} is a vector value representative of thecurrent from phase C to phase A at the source 200, {right arrow over(V_(B))} is a vector value of the voltage from phase B to neutral,{right arrow over (I_(BN))} is a vector value representative of thecurrent from phase B to neutral at the source 200, {right arrow over(V_(A))} is a vector value of the voltage from phase A to neutral, and{right arrow over (I_(AN))} is a vector value representative of thecurrent from phase A to neutral at the source 200.

The voltage vectors

$\overset{\rightarrow}{V_{CB}},\overset{\rightarrow}{V_{CA}},\overset{\rightarrow}{V_{B}},\overset{\rightarrow}{V_{A}}$

may readily be determined in any suitable manner based on the digitalmeasurement signals V_(A)(s), V_(B)(s), and V_(C)(s) received from theADC circuit 114. The current vectors

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

are determined as described below:

$\begin{matrix}{\overset{\rightarrow}{I_{CB}} = {{\frac{1}{6}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{B}}} + {\frac{1}{2}{\overset{\rightharpoonup}{I_{C}}.}}}} & (15) \\{\overset{\rightarrow}{I_{CA}} = {{\frac{1}{6}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{A}}} + {\frac{1}{2}{\overset{\rightharpoonup}{I_{C}}.}}}} & (16) \\{\overset{\rightarrow}{I_{BN}} = {{\frac{5}{6}\overset{\rightharpoonup}{I_{B}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{A}}} + {\frac{1}{2}{\overset{\rightharpoonup}{I_{C}}.}}}} & (17) \\{\overset{\rightarrow}{I_{AN}} = {{\frac{5}{6}\overset{\rightharpoonup}{I_{A}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{B}}} + {\frac{1}{2}{\overset{\rightharpoonup}{I_{C}}.}}}} & (18)\end{matrix}$

It can be seen that source or arithmetic SVA does not equal load orvector vector_VA in this case. The vector equations for determining SVAare based on the assumption that the internal resistance on each leg ofthe source 200 is relatively similar. It will further be appreciatedthat the calculation of source VA or SVA as described above does notrequire a neutral current measurement.

It will be appreciated that if the current measurement I_(N) is readilyavailable, then alternative versions of the above referenced equationsmay be used. In fact, so long as vector values for any three of thecurrents I_(A), I_(B), I_(C), I_(N) are available at the load 201 (oranywhere), values representative of the vector currents

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

at the source can be generated. In particular, the current vectors,

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

may alternatively be determined implementing the following vectorequations:

$\begin{matrix}{\overset{\rightarrow}{I_{CB}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{A}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{2}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (19) \\{\overset{\rightarrow}{I_{CA}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{B}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{2}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (20) \\{\overset{\rightarrow}{I_{BN}} = {{\frac{2}{3}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (21) \\{\overset{\rightarrow}{I_{AN}} = {{\frac{2}{3}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (22)\end{matrix}$

In another alternative, using only I_(A), I_(C) and I_(N), the currentvectors,

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

may also be determined:

$\begin{matrix}{\overset{\rightarrow}{I_{CB}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{A}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{2}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (23) \\{\overset{\rightarrow}{I_{CA}} = {{{- \frac{1}{3}}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (24) \\{\overset{\rightarrow}{I_{BN}} = {{{- \frac{2}{3}}\overset{\rightharpoonup}{I_{A}}} - {\frac{5}{6\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (25) \\{\overset{\rightarrow}{I_{AN}} = {{\frac{2}{3}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (26)\end{matrix}$

In yet another alternative, using only I_(B), I_(C) and I_(N), thecurrent vectors,

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

may also be determined:

$\begin{matrix}{\overset{\rightarrow}{I_{CB}} = {{{- \frac{1}{3}}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (27) \\{\overset{\rightarrow}{I_{CA}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{B}}} + {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{2}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (28) \\{\overset{\rightarrow}{I_{BN}} = {{\frac{2}{3}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{6\;}\overset{\rightharpoonup}{I_{N}}} + {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (29) \\{\overset{\rightarrow}{I_{AN}} = {{{- \frac{2}{3}}\overset{\rightharpoonup}{I_{B}}} - {\frac{5}{6\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{1}{3}{\overset{\rightharpoonup}{I_{C}}.}}}} & (30)\end{matrix}$

In still another embodiment using only I_(A), I_(B) and I_(N), thecurrent vectors,

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}}$

may also be determined:

$\begin{matrix}{\overset{\rightarrow}{I_{CB}} = {{{- \frac{1}{3}}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{2\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{2}{3}{\overset{\rightharpoonup}{I_{B}}.}}}} & (31) \\{\overset{\rightarrow}{I_{CA}} = {{{- \frac{1}{3}}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{2\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{2}{3}{\overset{\rightharpoonup}{I_{A}}.}}}} & (32) \\{\overset{\rightarrow}{I_{BN}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{B}}} - {\frac{1}{2\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{1}{3}{\overset{\rightharpoonup}{I_{A}}.}}}} & (33) \\{\overset{\rightarrow}{I_{AN}} = {{\frac{1}{3}\overset{\rightharpoonup}{I_{A}}} - {\frac{1}{2\;}\overset{\rightharpoonup}{I_{N}}} - {\frac{1}{3}{\overset{\rightharpoonup}{I_{B}}.}}}} & (34)\end{matrix}$

It will be appreciated that equation (14) employs the magnitudes of thevarious vector values discussed above. The processing circuit 116actually generates the magnitudes of the vector values

$\overset{\rightarrow}{I_{CB}},\overset{\rightarrow}{I_{CA}},\overset{\rightarrow}{I_{BN}},{{and}\mspace{20mu} \overset{\rightarrow}{I_{AN}}},$

such as those used in equation (14), using the following steps:obtaining contemporaneous samples of the relevant three or four ofI_(A), I_(B), I_(C), I_(N), adding the contemporaneous samples inaccordance with the relevant four equations of the equations (15) to(34), squaring the sum, repeating the above and accumulating the squaredsum values over several sample times, and then taking the square-root.

For example, FIGS. 3A-3C show an exemplary set of operations of theprocessing circuit 116 of the meter 10 including those that determineSVA per equation (14), using the values of equations (15)-(18) forgenerating the magnitude of the source currents current values {rightarrow over (I_(CB))}, {right arrow over (I_(CA))}, {right arrow over(I_(BN))}, and {right arrow over (I_(AN))}. It will be appreciated thatthe operations of FIGS. 3A-3C may readily by modified to implement anyof the equations (19)-(34) in obtaining a solution for equation (14).The operations of FIG. 3A-3C further show, at least in context theprocessing of samples to generate other metering values. As noted above,the processing circuit 116 preferably generates multiple meteringvalues, such as watt-hr, VAR-hr, RMS voltage, RMS current, as well asthe VA calculations.

Referring now to FIG. 3A, in step 302, the processing circuit 116obtains contemporaneous samples V_(A)(s), V_(B)(s), V_(C)(s), I_(A)(s),I_(B)(s), I_(C)(s) for a sample time s. To this end, the processingcircuit 116 obtains samples of the V_(A)(s), V_(B)(s), V_(C)(s),I_(A)(s), I_(B)(s) and I_(C)(s) from the ADC circuit 114. The processingcircuit 116 then proceeds to step 304. In step 304, the processingcircuit 116 generates source current samples I_(CB)(s), I_(CA)(s),I_(BN)(s) and I_(AN)(s) for the sample time s based on the equations(15)-(18). Specifically, the processing circuit 116 performs thefollowing calculations:

I _(CB)(s)=⅙I _(A)(s)−⅙I _(B)(s)+½I _(C)(s)  (35)

I _(CA)(s)=⅙I _(B)(s)−⅙I _(A)(s)+½I _(C)(s)  (36)

I _(BN)(s)=⅚I _(B)(s)+⅙I _(A)(s)+½I _(C)(s)  (37)

I _(AN)(s)=⅚I _(A)(s)+⅙I _(B)(s)+½I _(C)(s)  (38)

In step 306, the processing circuit 116 further generates thecontemporaneous samples of the V_(CB) and V_(CA) using the equations:

V _(CB)(s)=V _(C)(s)−V _(B)(s)  (39)

V _(CA)(s)=V _(C)(s)−V _(A)(s)  (40)

Thereafter, the processing circuit 116 proceeds to step 308. In step308, the processing circuit 116 squares each of the values generated insteps 304 and 306, as well as V_(B)(s) and V_(A)(s), and adds theresulting squared value of to an ongoing accumulation of correspondingvalues, I_(CBT), I_(CAT), I_(BNT), I_(ANT), V_(CBT), V_(CAT), V_(BT),V_(AT). In other words, the processing circuit performs the followingoperations:

I _(CBT) =I _(CBT) +[I _(CB)(s)]²  (40)

I _(CAT) =I _(CAT) +[I _(CA)(s)]²  (41)

I _(BNT) =I _(BNT) +[I _(BN)(s)]²  (42)

I _(ANT) =I _(ANT) +[I _(AN)(s)]²  (43)

V _(CB3T) =V _(CBT) +[V _(CB)(s)]²  (44)

V _(CAT) =V _(CAT) +[V _(CA)(s)]²  (45)

V _(BT) =V _(BT) +[V _(B)(s)]²  (46)

V _(AT) =V _(AT) +[V _(A)(s)]²  (47)

Thereafter, in step 310, the processing circuit 116 makes furthercalculations for the purposes of generating (i.e. updating) other energyconsumption values, such as those representative of watts, watt-hours,RMS current, RMS voltage and the like. The calculation of such valuesbased on the ongoing sample stream of V_(A)(s), V_(B)(s), V_(C)(s),I_(A)(s), I_(B)(s), I_(C)(s) is known in the art and may take differentformats. The processing circuit 116 may also calculate load VA or vectorVA as discussed further above.

Thereafter, in step 312, the processing circuit 116 increments a counterx. The counter x is used to determine whether to actually perform thenext SVA calculation, as will be discussed below. In particular, it isuseful to have samples from multiple cycles of the AC waveform beforecalculating the SVA value. After step 312, the processing circuit 116proceeds to step 314.

In step 314, the processing circuit 116 determines whether x is greaterthan a sample threshold sp. If not, then the processing circuit 116returns to step 302 and awaits the next set of samples V_(A)(s),V_(B)(s), V_(C)(s), I_(A)(s), I_(B)(s), I_(C)(s), wherein s has beenincremented for the next sampling period of the ADC 114. In thisembodiment, the value of sp is 504, and the sampling rate (ssec) is2520, which produces a measurement period of 200 ms.

If, however, the processing circuit 116 determines that x is greaterthan a sample threshold sp, then the processing circuit 116 proceeds tostep 316 to begin the source VA calculation. Specifically, in step 316,the processing circuit 116 generates the following vector magnitudevalues:

$\begin{matrix}{{\overset{\rightharpoonup}{I_{CB}}} = \sqrt{\frac{I_{CBT}}{sp}}} & (48) \\{{\overset{\rightharpoonup}{I_{CA}}} = \sqrt{\frac{I_{CAT}}{sp}}} & (49) \\{{\overset{\rightharpoonup}{I_{BN}}} = \sqrt{\frac{I_{BNT}}{sp}}} & (50) \\{{\overset{\rightharpoonup}{I_{AN}}} = \sqrt{\frac{I_{ANT}}{sp}}} & (51) \\{{\overset{\rightharpoonup}{V_{CB}}} = \sqrt{\frac{V_{CBT}}{sp}}} & (52) \\{{\overset{\rightharpoonup}{V_{CA}}} = \sqrt{\frac{V_{CAT}}{sp}}} & (53) \\{{\overset{\rightharpoonup}{V_{B}}} = \sqrt{\frac{V_{BT}}{sp}}} & (54) \\{{\overset{\rightharpoonup}{V_{A}}} = \sqrt{\frac{V_{AT}}{sp}}} & (55)\end{matrix}$

After step 316, the processing circuit 116 proceeds to step 318.

In step 318, the processing circuit 116 resets the counter x to zero,and also resets the values I_(CBT), I_(CAT), I_(BNT), I_(ANT), V_(CBT),V_(CAT), V_(BT), V_(AT) to zero. The processing circuit 116 thereafterproceeds to step 320. In step 320, the processing circuit 116 performsthe calculation of equation (14) based on the values generated in step316. In other words the processing circuit 116 generates SVA as follows:

SVA=VA=|{right arrow over (V _(CB))}|*|{right arrow over (I_(CB))}|+|{right arrow over (V _(CA))}|*|{right arrow over (I_(CA))}|+|{right arrow over (V _(B))}|*|{right arrow over (I_(BN))}|+|{right arrow over (V _(A))}|*|{right arrow over (I_(AN))}|  (14)

Thereafter, in step 322, the processing circuit 116 stores, displays orotherwise communicates the determined SVA value. In particular, theprocessing circuit 116 may suitably store the SVA value in the datastore 112, display the SVA value using the display 120, and/orcommunicate the SVA value to a remote device, such as a utilitycomputer, not shown, using the communication circuit 118.

The processing circuit 116 may employ the stored SVA value for furthercalculations. For example, the processing circuit 116 may further filterthe SVA value by averaging several consecutive SVA values, such as fiveor ten of such values. In some embodiments, it is the average SVA valuethat is displayed or communicated.

The processing circuit 116 may also accumulate the stored SVA valuescalculated over time, multiplied by the corresponding time periods, togenerate a source VA-hr value. The processing circuit 116 may also storein the memory 116 an SVA value for each of a plurality of time periodsin conjunction with a time-of-use metering function. In such a case, theprocessing circuit 116 stores either an average SVA (VA), or anaccumulated SVA (VAh), for each time period of a set of time periods foreach day.

In any event, after step 322, the processing circuit 116 returns to step302 and proceeds accordingly.

It will be appreciated that the embodiment described above may readilybe adapted to calculate source VA for a three-wire delta electricalservice. A three-wire delta service is similar to a four-wire deltaservice except that no separate neutral line is provided. Instead, thephase B line 214 is used as the neutral line.

To adapt the calculations discussed above for three-wire delta, theprocessing circuit 116 can use equation (14) set forth above, and any ofthe sets of equations discussed above, wherein I_(B) is set to−I_(A)−I_(C) (e.g. I_(B)(s)=I_(A)(s)−I_(C)(s)) and I_(N)=0. While asuitable method for calculating source VA in a three-wire delta systemis disclosed in U.S. Pat. No. 7,747,400, the embodiment described hereinallows for the same general sets of equations to be used for boththree-wire delta and four-wire delta systems, with only two extra (andsimple) operations added. As a result, the meter 10 can be readily madeadaptable to both systems with effectively one set of equations.

It will be appreciated that the processing circuit 116 of the meter 10may also provide load VA as well as any other energy consumption-relatedvalues to the display 120 or to the communication circuit 118 fortransmission to an external device. In some cases, the processingcircuit 116 provides the VA information to a billing calculation unit(such as a billing formula implemented by the processing circuit itself)so that billing calculations may be made, for example, in a conventionalmanner.

It will be appreciated that the above describe embodiments are merelyillustrative, and that those of ordinary skill in the art may readilydevise their own modifications and implementations that incorporate theprinciples of the present invention and fall within the spirit and scopethereof.

I claim:
 1. An arrangement in a meter connected between a source and aload, comprising: a) an A/D converter configured to generate digitalsamples of voltage and current waveforms in a polyphase electricalsystem; b) a processing circuit operably coupled to receive the digitalsamples from the A/D converter, the processing circuit configured to: i)obtain contemporaneous samples of V_(A), V_(B), V_(C), and at leastthree of I_(A), I_(B), I_(C), and I_(N), where I_(A) is a currentmeasurement signal of phase A, I_(B) is a current measurement signal ofphase B, k is a current measurement signal of phase C, I_(N) is acurrent measurement signal of a neutral connection, V_(A) is a voltagemeasurement signal from phase A to neutral, V_(B) is a voltagemeasurement signal from phase B to neutral, and V_(C) is a voltagemeasurement signal from phase C to neutral; ii) determine an I_(CB)sample value based on contemporaneous samples of at least three ofI_(A), I_(B), I_(C), and I_(N); iii) determine an I_(CA) sample valuebased on contemporaneous samples of at least three of I_(A), I_(B),I_(C), and I_(N); iv) determine an I_(BN) sample value based oncontemporaneous samples of at least three of I_(A), I_(B), I_(C), andI_(N); v) determine an I_(AN) sample value based on contemporaneoussamples of at least three of I_(A), I_(B), I_(C), and I_(N); vi)determine a VA value based at least in part on I_(CB), I_(CA), I_(BN)and I_(AN); and vii) provide information representative of the VAcalculation to one of a group consisting of a display, a communicationcircuit, a memory and a billing calculation unit.
 2. The arrangement ofclaim 1, wherein the processing circuit is further configured togenerate: a) The I_(CB) sample value based on the equation⅙I_(A)−⅙I_(B)+½I_(C); b) The I_(CA) sample value based on the equation⅙I_(B)−⅙I_(A)+½I_(C); c) The I_(BN) sample value based on the equation⅚I_(B)+⅙I_(A)+½I_(C); and d) The I_(AN) sample value based on theequation ⅚I_(A)+⅙I_(B)+½I_(C).
 3. The arrangement of claim 1, whereinthe processing circuit is further configured to: a) generate a pluralityof each of the I_(CB), I_(CA), I_(BN) and I_(AN) sample values; and b)generate a magnitude value for each of the plurality of the I_(CB),I_(CA), I_(BN) and I_(AN) sample values.
 4. The arrangement of claim 3,wherein the processing circuit is further configured to determine the VAvalue further based at least in part on the I_(CB) magnitude value, theI_(CA) magnitude value, the I_(BN) magnitude value, and the I_(AN)magnitude value.
 5. The arrangement of claim 4, wherein the processingcircuit is further configured to determine the VA value further based inpart on a magnitude of a voltage difference from phase C to phase B anda magnitude of a voltage difference from phase C to phase A.
 6. Thearrangement of claim 5, wherein the processing circuit is furtherconfigured to determine the magnitude of the voltage from phase C tophase B and determine the magnitude of the voltage from phase C to phaseA by: a) generating a plurality of the V_(CB) sample values, each V_(CB)sample value comprising a difference between a phase C sample and acontemporaneous phase B sample; and b) generating a V_(CB) magnitudevalue using the plurality of the V_(CB) sample values; c) generating aplurality of the V_(CA) sample values, each V_(CA) sample valuecomprising a difference between a phase C sample and a contemporaneousphase A sample; d) generating a V_(CA) magnitude value using theplurality of the V_(CA) sample values;
 7. The arrangement of claim 5,wherein the processing circuit is further configured to generate the VAvalue based on the equation:VA=|{right arrow over (V _(CB))}|*|{right arrow over (I _(CB))}|+|{rightarrow over (V _(CA))}|*|{right arrow over (I _(CA))}|+|{right arrow over(V _(B))}|*|{right arrow over (I _(BN))}|+|{right arrow over (V_(A))}|*|{right arrow over (I _(AN))}| wherein |{right arrow over(V_(CB))}| is the V_(CB) magnitude value, |{right arrow over (I_(CB))}|is the I_(CB) magnitude value, |{right arrow over (V_(CA))}| is theV_(CA) magnitude value, |{right arrow over (I_(CA))}| is the I_(CA)magnitude value, |{right arrow over (V_(B))}| is a magnitude of thevoltage from phase B to neutral, |{right arrow over (I_(BN))}| is theI_(BN) magnitude value, |{right arrow over (V_(A))}| is a magnitude ofthe voltage from phase A to neutral, and |{right arrow over (I_(AN))}|is a vector value representative of the current from phase A to neutral.8. The arrangement of claim 1, further comprising the display, andwherein the display is configured to display the informationrepresentative of the VA calculation.
 9. An arrangement in a meterconnected between a source and a load, comprising: a) an A/D converterconfigured to generate digital samples of voltage and current waveformsin a polyphase electrical system; b) a processing circuit operablycoupled to receive the digital samples from the A/D converter, theprocessing circuit configured to: i) obtain samples of V_(A), V_(B),V_(C), and at least three of I_(A), I_(B), I_(C), and I_(N), where I_(A)is a current measurement signal of phase A, I_(B) is a currentmeasurement signal of phase B, I_(C) is a current measurement signal ofphase C, I_(N) is a current measurement signal of a neutral connection,V_(A) is a voltage measurement signal from phase A to neutral, V_(B) isa voltage measurement signal from phase B to neutral, and V_(C) is avoltage measurement signal from phase C to neutral; ii) determine, basedon the obtained samples, a magnitude value |{right arrow over (V_(CB))}|of a voltage from phase C to phase B, a magnitude value |{right arrowover (I_(CB))}| of a source current from phase C to phase B, a magnitudevalue |{right arrow over (V_(CA))}| of a voltage from phase C to phaseA, a magnitude value |{right arrow over (I_(CA))}| of a source currentfrom phase C to phase A, a magnitude value |{right arrow over (V_(B))}|of a voltage from phase B to neutral, a magnitude value |{right arrowover (I_(BN))}| of a source current from phase B to neutral, a magnitudevalue |{right arrow over (V_(A))}| of a voltage from phase A to neutral,and a magnitude value |{right arrow over (I_(AN))}| of a source currentfrom phase A neutral. iii) generate the VA value based on the equationVA=|{right arrow over (V_(CB))}|*|{right arrow over (I _(CB))}|+|{rightarrow over (V _(CA))}|*|{right arrow over (I _(CA))}|+|{right arrow over(V _(B))}|*|{right arrow over (I _(BN))}|+|{right arrow over (V_(A))}|*|{right arrow over (I _(AN))}|; and iv) provide informationrepresentative of the VA calculation to one of a group consisting of adisplay, a communication circuit, a memory and a billing calculationunit.
 10. The arrangement of claim 9, wherein the processing circuit isfurther configured to determine the value |{right arrow over (I_(CB))}|based on samples of at least three of I_(A), I_(B), I_(C), and I_(N).11. The arrangement of claim 10, wherein the processing circuit isfurther configured to determine the value |{right arrow over (I_(CA))}|based on samples of at least three of I_(A), I_(B), I_(C), and I_(N).12. The arrangement of claim 9, wherein the processing circuit isfurther configured to determine the value |{right arrow over (I_(BN))}|based on samples of at least three of I_(A), I_(B), I_(C), and I_(N).13. The arrangement of claim 12, wherein the processing circuit isfurther configured to determine the value |{right arrow over (I_(AN))}|based on samples of at least three of I_(A), I_(B), I_(C), and I_(N).14. An arrangement in a meter connected between a source and a load,comprising: a) an A/D converter configured to generate digital samplesof voltage and current waveforms in a polyphase electrical system; b) aprocessing circuit operably coupled to receive the digital samples fromthe A/D converter, the processing circuit configured to: i) obtaincontemporaneous samples of V_(A), V_(B), V_(C), and at least three ofI_(A), I_(B), I_(C), and I_(N), where I_(A) is a current measurementsignal of phase A, I_(B) is a current measurement signal of phase B,I_(C) is a current measurement signal of phase C, I_(N) is a currentmeasurement signal of a neutral connection, V_(A) is a voltagemeasurement signal from phase A to neutral, V_(B) is a voltagemeasurement signal from phase B to neutral, and V_(C) is a voltagemeasurement signal from phase C to neutral; ii) determine a I_(CB)sample value based on contemporaneous samples of the at least three ofI_(A), I_(B), I_(C), and I_(N); iii) determine a VA value based at leastin part on I_(CB); and iv) provide information representative of the VAcalculation to one of a group consisting of a display, a communicationcircuit, a memory and a billing calculation unit.
 15. The arrangement ofclaim 14, wherein the processing circuit is further configured togenerate the I_(CB) sample value based on the equation⅙I_(A)−⅙I_(B)+½I_(C).
 16. The arrangement of claim 15, wherein theprocessing circuit is further configured to: generate a plurality of theI_(CB) sample values; generate a magnitude value of the plurality of theI_(CB) sample values; and determine the VA value based at least in parton the produce of the generated magnitude value and a magnitude of avoltage from phase C to phase B.